4 ms·

Is that true? I thought most instruments (or at least most pianos) these days were tuned to be equal tempered, so each scale would sound the same (modulo a pitc

by tgb 10y ago

Is that true? I thought most instruments (or at least most pianos) these days were tuned to be equal tempered, so each scale would sound the same (modulo a pitch scaling).

endymi0n 10y ago
Pianos actually often even employ a form of stretch tuning ( https://en.wikipedia.org/wiki/Stretched_tuning https://en.wikipedia.org/wiki/Stretched_tuning ) - which gets even more complex, as the OP only refers to sinus tones, which don't have any melodic overtones. Things get even more fun with this. Otherwise, you're right. Historic tunings often tried to optimize for a certain base scale (often times C major), while leaving behind a really bad sounding tuning at the other side of the circle of fifths ( https://en.wikipedia.org/wiki/Wolf_interval https://en.wikipedia.org/wiki/Wolf_interval ). Modern pianos are usually equal tempered, which is the strategy of leaving every scale equally bad off - but on the other hand being able to play in all keys without sounding too bad (The famous "well-tempered piano" is referring to this historic change in tuning strategies with small pieces written in all different kinds of keys, all of which would have sounded weird before). The more I learned about tuning, the more complex, beautiful and sad this topic became for me: http://blogs.scientificamerican.com/roots-of-unity/the-saddest-thing-i-know-about-the-integers/ http://blogs.scientificamerican.com/roots-of-unity/the-sadde... It's fascinating and even a little philosophical that we can get so close to perfection with the 12 step tuning - but never, ever completely attain it. By the way - That's part of the reason why choirs and orchestras often sound so good: As most other non-fixed-string instruments are able to do a slight adjustment in pitch, they can actually play perfect intervals in any chord, dynamically adjusting to any scale.
sgeisenh 10y ago
You're correct. Most instruments that lack real time tuning capabilities use equal temperament tuning, which is a 20th century development. Wind instruments are necessarily tuned to a specific key, due to the nature of the harmonic series. But most talented wind instrumentalists are capable of modifying pitch to be in tune in any key or chord. Down the rabbit hole, read on at your own peril: Even string instruments are tuned to a key, to a certain extent, due to the use of harmonics. It is possible to fine tune the pitch of a harmonic by shortening the string as usual, but it is exceedingly difficult, since shortening the string changes the position of the nodes (the spots on the string that must be touched in order to produce harmonics).
edejong 10y ago
That's the ideal, given infinitely long and infinitely bendable strings. Reality is that a tuner works from a certain key and tunes in equal temperament the other keys. Since the piano and the tuning is a compromise and there is limited time, the piano will always sound slightly better in one key than another. As most people play in keys close to the C major scale, this usually gets most attention. Also, pianos rely on resonation. I would not be surprised that the sound board and resonant cavity is designed to favour certain tones. I'm not certain about this though.

by tgb 10y ago

Is that true? I thought most instruments (or at least most pianos) these days were tuned to be equal tempered, so each scale would sound the same (modulo a pitch scaling).

endymi0n 10y ago

Pianos actually often even employ a form of stretch tuning ( https://en.wikipedia.org/wiki/Stretched_tuning https://en.wikipedia.org/wiki/Stretched_tuning ) - which gets even more complex, as the OP only refers to sinus tones, which don't have any melodic overtones. Things get even more fun with this. Otherwise, you're right. Historic tunings often tried to optimize for a certain base scale (often times C major), while leaving behind a really bad sounding tuning at the other side of the circle of fifths ( https://en.wikipedia.org/wiki/Wolf_interval https://en.wikipedia.org/wiki/Wolf_interval ). Modern pianos are usually equal tempered, which is the strategy of leaving every scale equally bad off - but on the other hand being able to play in all keys without sounding too bad (The famous "well-tempered piano" is referring to this historic change in tuning strategies with small pieces written in all different kinds of keys, all of which would have sounded weird before). The more I learned about tuning, the more complex, beautiful and sad this topic became for me: http://blogs.scientificamerican.com/roots-of-unity/the-saddest-thing-i-know-about-the-integers/ http://blogs.scientificamerican.com/roots-of-unity/the-sadde... It's fascinating and even a little philosophical that we can get so close to perfection with the 12 step tuning - but never, ever completely attain it. By the way - That's part of the reason why choirs and orchestras often sound so good: As most other non-fixed-string instruments are able to do a slight adjustment in pitch, they can actually play perfect intervals in any chord, dynamically adjusting to any scale.

sgeisenh 10y ago

You're correct. Most instruments that lack real time tuning capabilities use equal temperament tuning, which is a 20th century development. Wind instruments are necessarily tuned to a specific key, due to the nature of the harmonic series. But most talented wind instrumentalists are capable of modifying pitch to be in tune in any key or chord. Down the rabbit hole, read on at your own peril: Even string instruments are tuned to a key, to a certain extent, due to the use of harmonics. It is possible to fine tune the pitch of a harmonic by shortening the string as usual, but it is exceedingly difficult, since shortening the string changes the position of the nodes (the spots on the string that must be touched in order to produce harmonics).

edejong 10y ago

That's the ideal, given infinitely long and infinitely bendable strings. Reality is that a tuner works from a certain key and tunes in equal temperament the other keys. Since the piano and the tuning is a compromise and there is limited time, the piano will always sound slightly better in one key than another. As most people play in keys close to the C major scale, this usually gets most attention. Also, pianos rely on resonation. I would not be surprised that the sound board and resonant cavity is designed to favour certain tones. I'm not certain about this though.